Masters G.M. Renewable and Efficient Electric Power Systems

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328 WIND POWER SYSTEMS

so the overall efﬁciency of the wind turbine, from wind to electricity, is

Overall efﬁciency =

600 kW

2112 kW

= 0.284 = 28.4%

Notice that if the rotor itself is about 43% efﬁcient, as Fig. 6.11 suggests,

then the efﬁciency of the gear box times the efﬁciency of the generator

would be about 66% (43% × 66% = 28.4%).

The answers derived in the above example are fairly typical for large wind

turbines. That is, a large turbine will spin at about 20–30 rpm; the gear box will

speed that up by roughly a factor of 50–70; and the overall efﬁciency of the

machine is usually in the vicinity of 25–30%. In later sections of the chapter,

we will explore these factors more carefully.

6.6 WIND TURBINE GENERATORS

The function of the blades is to convert kinetic energy in the wind into rotating

shaft power to spin a generator that produces electric power. Generators consist

of a rotor that spins inside of a stationary housing called a stator. Electricity is

created when conductors move through a magnetic ﬁeld, cutting lines of ﬂux

and generating voltage and current. While small, battery-charging wind turbines

use dc generators, grid-connected machines use ac generators as described in the

following sections.

6.6.1 Synchronous Generators

In Chapter 3, the operation of synchronous generators, which produce almost

all of the electric power in the world, were described. Synchronous generators

are forced to spin at a precise rotational speed determined by the number of

poles and the frequency needed for the power lines. Their magnetic ﬁelds are

created on their rotors. While very small synchronous generators can create the

needed magnetic ﬁeld with a permanent magnet rotor, almost all wind turbines

that use synchronous generators create the ﬁeld by running direct current through

windings around the rotor core.

The fact that synchronous generator rotors needs dc current for their ﬁeld

windings creates two complications. First, dc has to be provided, which usually

means that a rectifying circuit, called the exciter, is needed to convert ac from

the grid into dc for the rotor. Second, this dc current needs to make it onto the

spinning rotor, which means that slip rings on the rotor shaft are needed, along

with brushes that press against them. Replacing brushes and cleaning up slip rings

adds to the maintenance needed by these synchronous generators. Figure 6.12

shows the basic system for a wind turbine with a synchronous generator, including

WIND TURBINE GENERATORS 329

Blades

Synchronous generator

Gear box

Φ ac output

ac input

Slip rings

Brushes

Exciter

Figure 6.12 A three-phase synchronous generator needs dc for the rotor windings, which

usually means that slip rings and brushes are needed to transfer that current to the rotor

from the exciter.

a reminder that the generator and blades are connected through a gear box to

match the speeds required of each.

6.6.2 The Asynchronous Induction Generator

Most of the world’s wind turbines use induction generators rather than the syn-

chronous machines just described. In contrast to a synchronous generator (or

motor), induction machines do not turn at a ﬁxed speed, so they are often

described as asynchronous generators. While induction generators are uncom-

mon in power systems other than wind turbines, their counterpart, induction

motors, are the most prevalent motors around—using almost one-third of all the

electricity generated worldwide. In fact, an induction machine can act as a motor

or generator, depending on whether shaft power is being put into the machine

(generator) or taken out (motor). Both modes of operation, as a motor during

start-up and as a generator when the wind picks up, take place in wind turbines

with induction generators. As a motor, the rotor spins a little slower than the

synchronous speed established by its ﬁeld windings, and in its attempts to “catch

up” it delivers power to its rotating shaft. As a generator, the turbine blades spin

the rotor a little faster than the synchronous speed and energy is delivered into

its stationary ﬁeld windings.

The key advantage of asynchronous induction generators is that their rotors

do not require the exciter, brushes, and slip rings that are needed by most syn-

chronous generators. They do this by creating the necessary magnetic ﬁeld in

the stator rather than the rotor. This means that they are less complicated and

less expensive and require less maintenance. Induction generators are also a little

more forgiving in terms of stresses to the mechanical components of the wind

turbine during gusty wind conditions.

330 WIND POWER SYSTEMS

Rotating Magnetic Field. To understand how an induction generator or motor

works, we need to introduce the concept of a rotating magnetic ﬁeld. Begin

by imagining coils imbedded in the stator of a three-phase generator as shown

in Fig. 6.13. These coils consist of copper conductors running the length of

the stator, looping around, and coming back up the other side. We will adopt

the convention that positive current in any phase means that current ﬂows from

the unprimed letter to the primed one (e.g., positive i

means that current ﬂows

from A to A



). When current in a phase is positive, the resulting magnetic ﬁeld

is drawn with a bold arrow; when it is negative, a dashed arrow is used. And

remember the arrow symbolism: a “+” at the end of a wire means current ﬂow

into the page, while a dot means current ﬂow out of the page.

Now, consider the magnetic ﬁelds that result from three-phase currents ﬂowing

in the stator. In Fig. 6.14a, the clock is stopped at ωt = 0, at which point i

reaches its maximum positive value, and i

and i

are both negative and equal

in magnitude. The magnetic ﬂux for each of the three currents is shown, the

sum of which is a ﬂux arrow that points vertically downward. A while later, let

us stop the clock at ωt = π/3 = 60

◦

.Nowi

= i

and both are positive, while

is now its maximum negative value, as shown in Fig. 6.14b. The resultant

sum of the ﬂuxes has now rotated 60

◦

in the clockwise direction. We could

continue this exercise for increasing values of ωt and we would see the resultant

ﬂux continuing to rotate around. This is an important concept for the inductance

generator: With three-phase currents ﬂowing in the stator, a rotating magnetic

ﬁeld is created inside the generator. The ﬁeld rotates at the synchronous speed

determined by the frequency of the currents f and the number of poles p.

That is, N

= 120f/p, as was the case for a synchronous generator.

The Squirrel Cage Rotor. A three-phase induction generator must be supplied

with three-phase ac currents, which ﬂow through its stator, establishing the rotat-

ing magnetic ﬁeld described above. The rotor of many induction generators (and

motors) consists of a number of copper or aluminum bars shorted together at their

ends, forming a cage not unlike one you might have to give your pet rodent some

′

Positive current Negative current

′

Figure 6.13 Nomenclature for the stator of an inductance generator. Positive current

ﬂow from A to A



results in magnetic ﬂux 

represented by a bold arrow pointing

downward. Negative current (from A



to A) results in magnetic ﬂux represented by a

dotted arrow pointing up.

WIND TURBINE GENERATORS 331

(a)

′

= 0

(b)

′

= p/3

Figure 6.14 (a) At ωt = 0,i

is a positive maximum while i

and i

are both negative

and equal to each other. The resulting sum of the magnetic ﬂuxes points straight down;

(b) at ωt = π/3, the magnetic ﬂux vectors appear to have rotated clockwise by 60

◦

exercise. They used to be called “squirrel” cage rotors, but now they are just cage

rotors. The cage is then imbedded in an iron core consisting of thin (0.5 mm)

insulated steel laminations. The laminations help control eddy current losses (see

Section 1.8.2). Figure 6.15 shows the basic relationship between stator and rotor,

which can be thought of as a pair of magnets (in the stator) spinning around the

cage (rotor).

To understand how the rotating stator ﬁeld interacts with the cage rotor, con-

sider Fig. 6.16a. The rotating stator ﬁeld is shown moving toward the right, while

the conductor in the cage rotor is stationary. Looked at another way, the stator

ﬁeld can be thought to be stationary and, relative to it, the conductor appears

to be moving to the left, cutting lines of magnetic ﬂux as shown in Fig. 6.16b.

Faraday’s law of electromagnetic induction (see Section 1.6.1) says that when-

ever a conductor cuts ﬂux lines, an emf will develop along the conductor and,

if allowed to, current will ﬂow. In fact, the cage rotor has thick conductor bars

with very little resistance, so lots of current can ﬂow easily. That rotor current,

labeled i

in Fig. 6.16b, will create its own magnetic ﬁeld, which wraps around

332 WIND POWER SYSTEMS

Magnetic field created in

stator appears to rotate

Cage

rotor

Figure 6.15 A cage rotor consisting of thick, conducting bars shorted at their ends,

around which circulates a rotating magnetic ﬁeld.

Moving stator field

Stationary cage

conductor

(a)

FORCE

Relative

conductor

motion

Stator field

(b)

Figure 6.16 In (a) the stator ﬁeld moves toward the right while the cage rotor conductor

is stationary. As shown in (b), this is equivalent to the stator ﬁeld being stationary while

the conductor moves to the left, cutting lines of ﬂux. The conductor then experiences a

force that tries to make the rotor want to catch up to the stator’s rotating magnetic ﬁeld.

the conductor. The rotor’s magnetic ﬁeld then interacts with the stator’s magnetic

ﬁeld, producing a force that attempts to drive the cage conductor to the right. In

other words, the rotor wants to spin in the same direction that the rotating stator

ﬁeld is revolving—in this case, clockwise.

The Inductance Machine as a Motor. Since it is easier to understand an

induction motor than an induction generator, we’ll start with it. The rotating

magnetic ﬁeld in the stator of the inductance machine causes the rotor to spin in

the same direction. That is, the machine is a motor—an induction motor. Notice

that there are no electrical connections to the rotor; no slip rings or brushes are

required. As the rotor approaches the synchronous speed of the rotating magnetic

ﬁeld, the relative motion between them gets smaller and smaller and less and less

force is exerted on the rotor. If the rotor could move at the synchronous speed,

there would be no relative motion, no current induced in the cage conductors, and

no force developed to keep the rotor going. Since there will always be friction to

WIND TURBINE GENERATORS 333

Slip

Torque

Breakdown torque

Braking

Linear region,

motoring

Figure 6.17 The torque– slip curve for an inductance motor.

overcome, the induction machine operating as a motor spins at a rate somewhat

slower than the synchronous speed determined by the stator. This difference in

speed is called slip, which is deﬁned mathematically as

s =

− N

= 1 −

(6.28)

where s is the rotor slip, N

is the no-load synchronous speed = 120f/p rpm,

where f is frequency and p is poles, and N

is the rotor speed.

As the load on the motor increases, the rotor slows down, increasing the

slip, until enough torque is generated to meet the demand. In fact, for most

induction motors, slip increases quite linearly with torque within the usual range

of allowable slip. There comes a point, however, when the load exceeds what is

called the “breakdown torque” and increasing the slip no longer satisﬁes the load

and the rotor will stop (Fig. 6.17). If the rotor is forced to rotate in the opposite

direction to the stator ﬁeld, the inductance machine operates as a brake.

Example 6.8 Slip for an induction motor A 60-Hz, four-pole induction

motor reaches its rated power when the slip is 4%. What is the rotor speed

at rated power?

The no-load synchronous speed of a 60-Hz, four-pole motor is

120f

120 × 60

= 1800 rpm

From (6.28) at a slip of 4%, the rotor speed would be

= (1 − s)N

= (1 − 0.04) · 1800 = 1728 rpm

The Inductance Machine as a Generator. When the stator is provided with

three-phase excitation current and the shaft is connected to a w ind turbine and

334 WIND POWER SYSTEMS

gearbox, the machine will start operation by motoring up toward its synchronous

speed. When the windspeed is sufﬁcient to force the generator shaft to exceed

synchronous speed, the induction machine automatically becomes a three-phase

generator delivering electrical power back to its stator windings. But where does

the three-phase magnetization current come from that started this whole pro-

cess? If it is grid-connected, the power lines provide that current. It is possible,

however, to have an induction generator provide its own ac excitation current

by incorporating external capacitors, which allows for power generation without

the grid.

The basic concept for a self-excited generator is to create a resonance condi-

tion between the inherent inductance of the ﬁeld windings in the stator and the

external capacitors that have been added. A capacitor and an inductor connected

in parallel form the basis for electronic oscillators; that is, they have a resonant

frequency at which they will spontaneously oscillate if given just a nudge in

that direction. That nudge is provided by a remnant magnetic ﬁeld in the rotor.

The oscillation frequency, and hence the rotor excitation frequency, depends on

the size of the external capacitors, which provides one way to control wind

turbine speed. In Fig. 6.18, a single-phase, self-excited, induction generator is

diagrammed showing the external capacitance.

So how fast does an inductance generator spin? The same slip factor deﬁnition

as was used for inductance motors applies [Eq. (6.28)], except that now the slip

will be a negative number since the rotor spins faster than synchronous speed.

For grid-connected inductance generators, the slip is normally no more than about

1%. This means, for example, that a two-pole, 60-Hz generator with synchronous

speed 3600 rpm will turn at about

= (1 − s)N

= [1 − (−0.01)] · 3600 = 3636 rpm

An added bonus with induction generators is they can cushion the shocks caused

by fast changes in wind speed. When the windspeed suddenly changes, the slip

increases or decreases accordingly, which helps absorb the shock to the wind

turbine mechanical equipment.

Load

Stator

inductance

External capacitance

added

Cage rotor

Figure 6.18 A self-excited inductance generator. External capacitors resonate with the

stator inductance causing oscillation at a particular frequency. Only a single phase

is shown.

SPEED CONTROL FOR MAXIMUM POWER 335

6.7 SPEED CONTROL FOR MAXIMUM POWER

In this section we will explore the role that the gear box and generator have

with regard to the rotational speed of the rotor and the energy delivered by the

machine. Later, we will describe the need for speed control of rotor blades to

be able to shed wind to prevent overloading the turbine’s electrical components

in highwinds.

6.7.1 Importance of Variable Rotor Speeds

There are other reasons besides shedding high-speed winds that rotor speed con-

trol is an important design task. Recall Fig. 6.11, in which rotor efﬁciency C

was shown to depend on the tip-speed ratio, TSR. Modern wind turbines oper-

ate best when their TSR is in the range of around 4–6, meaning that the tip

of a blade is moving 4–6-times the wind speed. Ideally, then, for maximum

efﬁciency, turbine blades should change their speed as the windspeed changes.

Figure 6.19 illustrates this point by showing an example of blade efﬁciency ver-

sus wind speed with three discrete steps in rotor rpm as a parameter. Unless the

rotor speed can be adjusted, blade efﬁciency C

changes as wind speed changes.

It is interesting to note, however, that C

is relatively ﬂat near its peaks so that

continuous adjustment of rpm is only modestly better than having just a few

discrete rpm steps available.

While Fig. 6.19 shows the impact of rotor speed on blade efﬁciency, what

is more important is electric power delivered by the wind turbine. Figure 6.20

15131197

0.0

0.1

0.2

0.3

0.4

0.5

Wind speed (m/s)

Blade efficiency,

20 rpm

30 rpm

40 rpm

Figure 6.19 Blade efﬁciency is improved if its rotation speed changes with changing

wind speed. In this ﬁgure, three discrete speeds are shown for a hypothetical rotor.

336 WIND POWER SYSTEMS

Wind speed (m/s)

151413121110987

100

200

300

400

500

20 rpm

30 rpm

40 rpm

Power delivered (kW)

Figure 6.20 Example of the impact that a three-step rotational speed adjustment has

on delivered power. For winds below 7.5 m/s, 20 rpm is best; between 7.5 and 11 m/s,

30 rpm is best; and above 11 m/s, 40 rpm is best.

shows the impact of varying rotor speed from 20 to 30 to 40 rpm for a 30-m

rotor with efﬁciency given in Fig. 6.19, along with an assumed gear and generator

efﬁciency of 70%.

While blade efﬁciency beneﬁts from adjustments in speed as illustrated in

Figs. 6.19 and 6.20, the generator may need to spin at a ﬁxed rate in order to

deliver current and voltage in phase with the grid that it is feeding. So, for

grid-connected turbines, the challenge is to design machines that can somehow

accommodate variable rotor speed and somewhat ﬁxed generator speed—or at

least attempt to do so. If the wind turbine is not grid-connected, the generator

electrical output can be allowed to vary in frequency (usually it is converted to

dc), so this dilemma isn’t a problem.

6.7.2 Pole-Changing Induction Generators

Induction generators spin at a frequency that is largely controlled by the number

of poles. A two-pole, 60-Hz generator rotates at very close to 3600 rpm; with

four poles it rotates at close to 1800 rpm; and so on. If we could change the

number of poles, we could allow the wind turbine to have several operating

speeds, approximating the performance shown in Figs. 6.19 and 6.20. A key to

this approach is that as far as the rotor is concerned, the number of poles in

the stator of an induction generator is irrelevant. That is, the stator can have

external connections that switch the number of poles from one value to another

without needing any change in the rotor. This approach is common in household

appliance motors such as those used in washing machines and exhaust fans to

give two- or three-speed operation.

SPEED CONTROL FOR MAXIMUM POWER 337

6.7.3 Multiple Gearboxes

Some wind turbines have two gearboxes with separate generators attached to

each, giving a low-wind-speed gear ratio and generator plus a high-wind-speed

gear ratio and generator.

6.7.4 Variable-Slip Induction Generators

A normal induction generator maintains its speed within about 1% of the syn-

chronous speed. As it turns out, the slip in such generators is a f unction of the

dc resistance in the rotor conductors. By purposely adding variable resistance to

the rotor, the amount of slip can range up to around 10% or so, which would

mean, for example, that a four-pole, 1800-rpm machine could operate anywhere

from about 1800 to 2000 rpm. One way to provide this capability is to have

adjustable resistors external to the generator, but the trade-off is that now an

electrical connection is needed between the rotor and resistors. That can mean

abandoning the elegant cage rotor concept and instead using a wound rotor with

slip rings and brushes similar to what a synchronous generator has. And that

means more maintenance will be required.

Another way to provide variable resistance for the rotor is to physically mount

the resistors and the electronics that are needed to control them on the rotor itself.

But then you need some way to send signals to the rotor telling it how much slip

to provide. In one system, called Opti Slip



, an optical ﬁber link to the rotor is

used for this communication.

6.7.5 Indirect Grid Connection Systems

In this approach, the wind turbine is allowed to spin at whatever speed that

is needed to deliver the maximum amount of power. When attached to a syn-

chronous or induction generator, the electrical output will have variable frequency

depending on whatever speed the wind turbine happens to have at the moment.

This means that the generator cannot be directly connected to the utility grid,

which of course requires ﬁxed 50- or 60-Hz current.

Figure 6.21 shows the basic concept of these indirect systems. Variable-

frequency ac from the generator is rectiﬁed and converted into dc using high-

power transistors. This dc is then sent to an inverter that converts it back to ac, but

this time with a steady 50- or 60-Hz frequency. The raw output of an inverter is

pretty choppy and needs to be ﬁltered to smooth it. As described in Chapter 2, any

time ac is converted to dc and back again, there is the potential for harmonics to

be created, so one of the challenges associated with these variable-speed, indirect

wind turbine systems is maintaining acceptable power quality.

In addition to higher annual energy production, variable-speed wind turbines

have an advantage of greatly minimizing the wear and tear on the whole system

caused by rapidly changing wind speeds. When gusts of wind hit the turbine,

rather than having a burst of torque hit the blades, drive shaft, and gearbox,